How to use this calculator
- Decimal → Fraction: type a decimal such as 1.625. For a repeating decimal, put the repeating digits in brackets (0.(3), 1.8(3)) or type them once and say how many repeat. Tick Round to the nearest fraction to also get the closest 1/16, 1/8 and so on.
- Fraction → Decimal: enter a numerator and denominator, plus a whole number for a mixed number.
- Percent → Fraction: enter a percentage such as 37.5.
Results update as you type, with the working shown. The calculator works with the exact digits you type, so there are no rounding errors, and nothing is saved.
How to convert a decimal to a fraction
- Write the decimal over 1.
- Multiply the top and bottom by 10 for each digit after the decimal point, so the top becomes a whole number.
- Simplify by dividing both by their greatest common factor (GCF).
- If the fraction is bigger than 1, you can write it as a mixed number.
Worked example: 2.625 has three decimal places, so multiply by 1,000: 2.625/1 = 2625/1000.
The GCF of 2625 and 1000 is 125, so 2625/1000 = 21/8. Since 21 ÷ 8 = 2 remainder 5, that is 2 5/8.
Negative decimals work the same way: convert the positive value, then put the minus sign back, so −0.4 = −4/10 = −2/5.
How to convert repeating decimals to fractions
A repeating decimal never ends, so you can’t just put it over a power of 10. Instead, use a little algebra to cancel out the endless tail:
- Call the number x.
- Multiply x by a power of 10 so that one whole repeating block moves past the decimal point.
- Subtract a copy of x whose digits after the point line up, so the repeating parts cancel.
- Solve for x and simplify.
0.666… → 2/3: let x = 0.666…. Then 10x = 6.666…. Subtracting, 10x − x = 6.666… − 0.666…, so 9x = 6 and x = 6/9 = 2/3.
0.1666… → 1/6: here only the 6 repeats. Let x = 0.1666…. Move the non-repeating 1 first: 10x = 1.666…. Then 100x = 16.666…. Subtracting, 100x − 10x = 16.666… − 1.666…, so 90x = 15 and x = 15/90 = 1/6.
How to convert a fraction to a decimal
Divide the numerator by the denominator. 5/8 = 5 ÷ 8 = 0.625. Some divisions never end: 1 ÷ 3 = 0.333…, because the same remainder keeps coming back in the long division, so the same digits repeat. A fraction in lowest terms gives an ending decimal only when its denominator has no prime factors other than 2 and 5. That’s why eighths, fifths and tenths end, but thirds, sixths and sevenths repeat.
How to convert a percent to a fraction
“Percent” means “out of 100”, so write the percentage over 100 and simplify. 12.5% = 12.5/100 = 125/1000 = 1/8. Percentages over 100 give fractions bigger than 1: 150% = 150/100 = 3/2 = 1 1/2.
Rounding to the nearest fraction
Tape measures and rulers in inches are marked in halves, quarters, eighths and sixteenths, so a measurement like 3.14159 inches is more useful as the nearest 1/16. Multiply by 16 (50.27), round to the nearest whole number (50), and put it back over 16: 50/16 = 3 1/8. The calculator also shows how far the rounded fraction is from your exact value.
Common conversions
| Decimal | Fraction | Percent |
|---|---|---|
| 0.1 | 1/10 | 10% |
| 0.125 | 1/8 | 12.5% |
| 0.2 | 1/5 | 20% |
| 0.25 | 1/4 | 25% |
| 0.333… | 1/3 | 33.333…% |
| 0.375 | 3/8 | 37.5% |
| 0.5 | 1/2 | 50% |
| 0.625 | 5/8 | 62.5% |
| 0.666… | 2/3 | 66.666…% |
| 0.75 | 3/4 | 75% |
| 0.8 | 4/5 | 80% |
| 0.875 | 7/8 | 87.5% |
Frequently asked questions
How do you convert a decimal to a fraction?
Write the decimal over 1, multiply the top and bottom by 10 for every digit after the decimal point, then simplify. For 0.75: 0.75/1 = 75/100, and dividing both by their GCF of 25 gives 3/4.
How do you turn a repeating decimal into a fraction?
Call the number x, multiply it by a power of 10 that shifts one full repeating block past the decimal point, and subtract the original so the repeating tails cancel. For x = 0.666…, 10x = 6.666…, so 10x − x = 6, 9x = 6 and x = 6/9 = 2/3.
How do I enter a repeating decimal in this calculator?
Put the repeating digits in brackets, such as 0.(3) for 0.333… or 0.1(6) for 0.1666…. Or type the digits once, like 0.36, and enter how many digits at the end repeat (2 gives 0.363636…).
What is 0.375 as a fraction?
0.375 = 375/1000. The GCF of 375 and 1000 is 125, so it simplifies to 3/8. As a percentage it is 37.5%.
Why does 0.999… equal 1?
Using the repeating-decimal method, x = 0.999… gives 10x = 9.999…, so 10x − x = 9, 9x = 9 and x = 1. There is no number between 0.999… and 1, so they are the same number written two ways.